Cars have space. A camp stove in the trunk and you can cook anything. Likewise a cooler and you can store things for a short time. Since you have a car you can drive to a supermarket regularly and thus not need to store anything for longer than the cooler can keep them fresh.

Food deserts don't exist if you have a car in any American city since it is never that far to a suburb. (if you don't have a car getting is much much harder)

I have done the above - as a contractor working in a place a significant distance from home on a short term job. There were a lot of people like me in the cheap hotels I was staying at. OTOH, none of us were homeless - the homeless generally have other issues making them homeless and so even though that options would be cheap and work that doesn't mean they would be able to do it